WASHINGTON — A measure of Americans who applied for unemployment benefits over the past month has fallen to its lowest level in almost six years, signaling fewer layoffs.

The Labor Department said today that the average number of people who applied for benefits over the past four weeks dropped 6,250 to 335,500. That’s the lowest level since November 2007, the month before the Great Recession began.

The four-week average smooths week to week fluctuations.

Weekly applications for unemployment aid increased by 5,000 last week to a seasonally adjusted 333,000. But that’s up only slightly from the previous week’s 5½-year low.

The decrease in the four-week average points to an encouraging trend for the job market. Applications, which are a proxy for layoffs, have fallen more than 10 percent since the start of the year. That’s helped drive net job gains this year, which show the number of people hired minus the number who lose or quit their jobs.

Economists were hopeful that the drop in layoffs could lead to some strengthening in the job market. Jennifer Lee, senior economist at BMO Capital Markets, called the decline in the four-week moving average “very good news indeed.”

But Bricklin Dwyer, an economist at BNP Paribas, cautioned that the unemployment claims figures so far have signaled only modest healing in the labor market.

“In terms of job growth, we have seen a disconnect between the level of hiring and firing,” Dwyer said.

Employers added 162,000 jobs last month, the fewest since March. And most of the job growth came in lower-paying industries or part-time work. Since January, the economy has added an average of 192,000 jobs a month, a solid number of net jobs.

It doesn’t take many hires to create a high net gain when employers are letting go of so few workers. But while employers are no longer cutting jobs, many remain reluctant to hire in the face of tax increases, federal spending cuts and slower global growth.

Layoffs have averaged 1.5 million a month this year through June, even fewer than the 1.77 million averaged in the pre-recession year of 2006.

But total hiring in June actually declined 289,000 to 4.2 million, the latest data available. That’s down from a year earlier and the biggest one-month drop in hiring since June 2010.

The unemployment rate fell in July to 4½-year low of 7.4 percent in July, down from 7.6 percent in June. That is still well above the 5 percent to 6 percent associated with a normal economy.

More than 4.5 million people received unemployment aid in the week ending July 20, the latest data available. That’s down 174,418 from the previous week. The number of recipients has fallen 21 percent in the past year.